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Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...
For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...
In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...
The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...
A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...
We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...
Compute memories are memory arrays augmented with dedicated logic to support arithmetic. They support the efficient execution of data-centric computing patterns, such as those characterizing Artificial Intelligence (AI) algorithms. These architectures can ...
